Consider Review Exercise 3.64 on page 107. There are two service lines. The random variables X and Y are the proportions of time that line 1 and line 2 are in use, respectively. The joint probability density function for (X,Y ) is given by f(x,y)=3 2(x2 + y2), 0 x, y 1, 0, elsewhere. (a) Determine whether or not X and Y are independent. (b) It is of interest to know something about the proportion of Z = X + Y , the sum of the two proportions. Find E(X + Y ). Also nd E(XY). (c) Find Var(X), Var(Y ), and Cov(X,Y ). (d) Find Var(X + Y ).

Tuesday, April 4 • Example 12: Sleeping Medication A research concludes that the number of hours of additional sleep by patients using Ambien increased on average by a statistically significant amount , 1.5 hours. What type of error might this be H :0 Ambien has no effect ; aH : Ambien increases sleep on average; rejected null a. This is a correct decision. The researchers concluded a significant increase in the number of hours of sleep, on av